Beard's family moved from Buffalo to Painesville, Ohio, during his youth. After a brief, and unsuccessful, apprenticeship to a watch-maker in Detroit, Michigan, Beard returned to Ohio where he became acquainted with an itinerant portrait painter. This meeting led to his first attempts in portraiture, painting likenesses of family and friends, and his determining on a career as an artist. In 1829 he traveled to Pittsburgh in hopes of finding patrons and developing his new vocation, but the venture proved unsuccessful. The next several years passed working at various jobs along the Ohio River. However, in 1833 he married and settled in Cincinnati, where he found the patrons he had long needed and established his reputation as a portraitist. In the following years he traveled extensively along the Ohio and Mississippi Rivers in search of commissions and was soon considered one of the leading portraitists working in the West; his sitters including such personages as John Quincy Adams, Henry Clay, and William Henry Harrison. In the late 1830s Beard expanded his range of subject matter to include animal and genre paintings, and frequently sent his works to New York where they were acquired and shown by the American Art-Union.
Having begun to establish a following in the East, Beard appears to have tried spending some time in New York. In 1846 and and 1847, the first occasions of his work being included in Academy annual exhibitions, his addresses given in the catalogues were in the city. That he had not established residence is clear from the minutes of the Annual Meeting of May 12,1847, where he is recorded as "J. H. Beard Painter Cincinnati" in the listing of newly elected honorary members. Despite this sign of welcome, he returned to Cincinnati, where he continued to work as an artist until 1861. During the Civil War he served as a captain on the staff of General Lew Wallace.
After the war, Beard was again in New York, joining his younger brother, William, and resumed his career as an artist, but returned to Ohio in 1866. Four years later he relocated to New York, this time to remain; he maintained a studio on Broadway throughout his life, increasingly concentrating on animal and genre painting. Beard's works were frequently exhibited in the annual exhibitions of the National Academy.